Quasi-elastic polarization-transfer measurements on the deuteron in anti-parallel kinematics

We present measurements of the polarization-transfer components in the H2(e→,e′p→) reaction, covering a previously unexplored kinematic region with large positive (anti-parallel) missing momentum, pmiss, up to 220MeV/c, and Q2=0.65 (GeV/c)2. These measurements, performed at the Mainz Microtron (MAMI), were motivated by theoretical calculations which predict small final-state interaction (FSI) effects in these kinematics, making them favorable for searching for medium modifications of bound nucleons in nuclei. We find in this kinematic region that the measured polarization-transfer components Px and Pz and their ratio agree with the theoretical calculations, which use free-proton form factor…

Polarization observables in deuteron photodisintegration below 360 MeV

High precision measurements of induced and transferred recoil proton polarization in d(polarized gamma, polarized p})n have been performed for photon energies of 277--357 MeV and theta_cm = 20 degrees -- 120 degrees. The measurements were motivated by a longstanding discrepancy between meson-baryon model calculations and data at higher energies. At the low energies of this experiment, theory continues to fail to reproduce the data, indicating that either something is missing in the calculations and/or there is a problem with the accuracy of the nucleon-nucleon potential being used.

Photon Scattering Off Nuclei

The study of nuclear and subnuclear structure by means of photon scattering is outlined. Besides a brief exposition of the formalism a few illustrative examples are discussed.

General Multipole Expansion of Polarization Observables in Deuteron Electrodisintegration

Formal expressions are derived for the multipole expansion of the structure functions of a general polarization observable of exclusive electrodisintegration of the deuteron using a longitudinally polarized beam and/or an oriented target. This allows one to exhibit explicitly the angular dependence of the structure functions by expanding them in terms of the small rotation matrices $d^j_{m'm}(\theta)$, whose coefficients are given in terms of the electromagnetic multipole matrix elements. Furthermore, explicit expressions for the coefficients of the angular distributions of the differential cross section including multipoles up to $L_{max}=3$ are listed in tabular form.

Relativistic corrections and unitary equivalence in elastic electron deuteron scattering.

The role of unitary equivalence of relativistic corrections in elastic electron deutron scattering is studied, starting from a class of approximately, unitarily equivalent Hamiltonians and using consistent charge density operators. The connection of various formal approaches for deriving the relativistic corrections to wave functions and operators are discussed in detail. For reasons of simplicity, we have chosen a pure one-pion-exchange model and calculated the charge and quadrupole form factors of the deuteron. The numerical results show that the unitary equivalence holds at small momentum transfers, but breaks down rather soon with increasing momentum transfers (\ensuremath{\lesssim}5 ${…

Precise Measurement of the Neutron Magnetic Form FactorGMnin the Few-GeV2Region

The neutron elastic magnetic form factor was extracted from quasielastic electron scattering on deuterium over the range Q;{2}=1.0-4.8 GeV2 with the CLAS detector at Jefferson Lab. High precision was achieved with a ratio technique and a simultaneous in situ calibration of the neutron detection efficiency. Neutrons were detected with electromagnetic calorimeters and time-of-flight scintillators at two beam energies. The dipole parametrization gives a good description of the data.

Hadron Structure Studied with the Electromagnetic Probe - from Giant Resonances to Meson Production

The development of theoretical photonuclear physics over the last 40 years is illustrated by a few selected examples highlighting a number of important issues like collective motion in nuclei, the role of subnuclear degrees of freedom, relativity and meson production.

Survey on polarization observables in deuteron photodisintegration below pion-production threshold

Polarization observables of deuteron photodisintegration with polarized photons and oriented deuterons are systematically investigated below π-production threshold with respect to their sensitivity to subnuclear degrees of freedom and relativistic effects, to the different electric and magnetic multipole contributions, and to various realistic potential models. In particular, a complete survey on all single- and double-polarization observables like beam and target asymmetries of the differential cross section, nucleon polarization and proton-neutron spin correlation is given.

Two-body effects in coherent η-meson photoproduction on the deuteron in the region of theS11(1535)resonance

Coherent \ensuremath{\eta}-meson photoproduction on the deuteron has been studied, where the emphasis is on the relative importance of two-body contributions from hadronic rescattering and electromagnetic meson exchange currents besides the impulse approximation. For the elementary photoproduction amplitude a coupled resonance model developed by Bennhold and Tanabe has been used that fits reasonably well with the experimental data. The rescattering effects are treated within a coupled channel approach considering the intermediate excitation of the ${P}_{11}(1440),$ ${D}_{13}(1520),$ and ${S}_{11}(1535)$ nucleon resonances. The hadronic interaction between nucleon and resonances is modeled b…

Spin Asymmetry and Gerasimov-Drell-Hearn Sum Rule for the Deuteron

An explicit evaluation of the spin asymmetry of the deuteron and the associated GDH sum rule is presented which includes photodisintegration, single and double pion and eta production as well. Photodisintegration is treated with a realistic retarded potential and a corresponding meson exchange current. For single pion and eta production the elementary operator from MAID is employed whereas for double pion production an effective Lagrangean approach is used. A large cancellation between the disintegration and the meson production channels yields for the explicit GDH integral a value of 27.31 $\mu$b to be compared to the sum rule value 0.65 $\mu$b.

Interaction effects in ${\bm K^+}$ photoproduction on the deuteron

Kaon photoproduction on the deuteron is studied with respect to a specific two-body contribution, namely a pion mediated production process, besides other final state interaction contributions from kaon-nucleon and hyperon-nucleon scattering. In this process, a pion is first photoproduced on one nucleon and then interacts with the spectator nucleon in a strangeness exchange reaction leading to a kaon and a hyperon. A sizeable effect from this pion mediated contribution is found, considerably larger than the previously studied hyperon-nucleon rescattering, whereas kaon-nucleon rescattering is much less important. Besides total and semi-inclusive differential cross sections, tensor target asy…

General formulae for polarization observables in two-body break-up of deuteron photodisintegration

The formal expressions of all possible polarization observables ind(γ,N)N with polarized photons and oriented deuterons are derived in terms of thet-matrix elements. Furthermore, using the multipole expansion of thet-matrix, all observables are expanded in terms of Legendre polynomials or associated functions, the coefficients of which are given as bilinear forms of the multipole moments and allow a model independent analysis of experimental data.

Coherent pion electroproduction on the deuteron in the Δ(1232) resonance region

Coherent pion electroproduction on the deuteron is studied in the Δ(1232) resonance region in the impulse approximation, i.e., neglecting pion rescattering and two-body effects. The elementary reaction on the nucleon is described in the framework of an effective Lagrangian approach including the dominant P33(1232) resonance and the usual background terms of the Born contributions for π0 production. We have studied the influence of these different contributions on the various structure functions which determine the unpolarized exclusive differential cross section in a variety of kinematic regions.

A coupled channel calculation of the double-?(1 236) component of the deuteron

TheΔΔ-component of the deuteron is calculated in a full coupled channel calculation including a diagonalΔ-Δ-interaction and compared to the impulse approximation. Without a diagonalΔ-Δ-interaction both methods give very similar results while inclusion of theΔ-Δ-interaction leads to a decrease of the (ΔΔ)-probability of about 25%. The main uncertainties originate from limited knowledge of coupling constants and cut-off ranges. Accordingly the (ΔΔ)-probability varies between 0.3 and 1 percent.

Relativistic Effects and the Role of Heavy Meson Exchange in Deuteron Photodisintegration

Relativistic effects and the role of heavy meson exchange in deuteron photodisintegration are studied systematically for photon energies below the pion production threshold. In a (p/M)-expansion, all leading order relativistic one-body and pi-exchange as well as all static heavy meson exchange currents consistent with the Bonn OBEPQ model are included. In addition, one- and two-body boost effects have been investigated. Sizeable effects from the various two-body contributions beyond pi-exchange have been found in almost every observable considered, i.e., differential cross section and single polarization observables.

Components of polarization-transfer to a bound proton in a deuteron measured by quasi-elastic electron scattering

We report the first measurements of the transverse (Px and Py) and longitudinal (Pz) components of the polarization transfer to a bound proton in the deuteron via the H2(e→,e′p→) reaction, over a wide range of missing momentum. A precise determination of the electron beam polarization reduces the systematic uncertainties on the individual components to a level that enables a detailed comparison to a state-of-the-art calculation of the deuteron using free-proton electromagnetic form factors. We observe very good agreement between the measured and the calculated Px/Pz ratios, but deviations of the individual components. Our results cannot be explained by medium modified electromagnetic form f…

The influence of Fermi motion on the comparison of the polarization transfer to a proton in elastic e→p and quasi-elastic e→A scattering

Abstract A comparison between polarization-transfer to a bound proton in quasi-free kinematics by the A ( e → , e ′ p → ) knockout reaction and that in elastic scattering off a free proton can provide information on the characteristics of the bound proton. In the past the reported measurements have been compared to those of a free proton with zero initial momentum. We introduce, for the first time, expressions for the polarization-transfer components when the proton is initially in motion and compare them to the 2H data measured at the Mainz Microtron (MAMI). We show the ratios of the transverse ( P x ) and longitudinal ( P z ) components of the polarization transfer in H 2 ( e → , e ′ p → …

Baryon resonances in nuclei

The field of baryon resonances in nuclei is reviewed. Theoretical developments and experimental evidence as well are discussed. Special emphasis is laid on electromagnetic processes for the two nucleon system. Some aspects of real isobars in nuclei are touched upon.

Tensor and Vector Analyzing Powers in the Reaction 2H(e,e’p)

The first experiment to be performed an the internal target facility of NIKHEF-K will be a study of eleclron-induced quasi-elastic proton knock-out from tensor-polarized deuterium. Here, we present the first results from the experimental tests as well as the results of a Monte Carlo simulation, which show the feasibility of the proposed experiment, even at modest luminosities.

Effect of three-body cluster on the healing properties of the Jastrow Correlation function

A variational equation for the Jastrow Correlation function is derived from the energy functional expanded up to three-body cluster terms. The asymptotic behaviour of this nonlinear equation is studied. The solutions show a healing at least of the type cos(tαr)/r2. The influence of higher cluster contributions is studied. Finally, it is discussed, how one can reduce the many-body cluster contributions to healing conditions to be used in the two-body cluster treatment.

Measurements of the induced polarization in the quasi-elastic A(e,e′p→) process in non-coplanar kinematics

Abstract We report measurements of the induced polarization P → of protons knocked out from 2H and 12C via the A ( e , e ′ p → ) reaction. We have studied the dependence of P → on two kinematic variables: the missing momentum p miss and the “off-coplanarity” angle ϕ p q between the scattering and reaction planes. For the full 360° range in ϕ p q , both the normal ( P y ) and, for the first time, the transverse ( P x ) components of the induced polarization were measured with respect to the coordinate system associated with the scattering plane. P x vanishes in coplanar kinematics, however in non-coplanar kinematics, it is on the same scale as P y . We find that the dependence on ϕ p q is si…

On the (ΔΔ)-component of the deuteron

Abstract The (ΔΔ)-component of the deuteron is investigated using π- and ϱ-exchange for the (NN → ΔΔ)-transition interaction. The depedence of the strength of the (ΔΔ)-component on thetype of regularization, the cut-off parameter and the normal deuteron wave functions is discussed. Inclusion of the ϱ-exchange leads to a weaker dependence on the cut-off parameter and to a smaller (ΔΔ)-admixture probability of 0.7 to 1.2 percent depending on the normal deuteron wave function for a cut-off parameter Λ = 5 fm−1.

Electromagnetic sum rules for light nuclei

Electromagnetic sum rules describe gross features of the electromagnetic structure of nuclei 1). A well known example is the Thomas-Reiche-Kuhn (TRK) sum rule, which relates the integrated total El-absorption cross section to the ground state expectation value of the double commutator of the dipole operator D with the nuclear Hamiltonian. While the k inet ic energy gives a model independent contr ibut ion, i . e . , the classical sum rule ~cl = 60 NZ/A MeV mb, the nuclear twobody potential gives an additional contr ibution in the presence of exchange and/or momentum dependent (or nonlocal) forces. In this case, I

Deuteron photodisintegration at low energies

All presently available experimental data on deuteron photodisintegration below 40 MeV (i.e., total and differential cross sections, photon asymmetry and neutron polarization) are collected and carefully compared with the present status of the conventional theory (i.e., in the framework of mesontheoretical or semi-phenomenologicalN-N potentials including subnuclear degrees of freedom and relativistic corrections). No significant evidence for a failure of the conventional theory is found within the present experimental accuracy.

Influence of Coulomb distortion on polarization observables in elastic electromagnetic lepton hadron scattering at low energies

The formal expression for the most general polarization observable in elastic electromagnetic lepton hadron scattering at low energies is derived for the nonrelativistic regime. For the explicit evaluation the influence of Coulomb distortion on various polarization observables is calculated in a distorted wave Born approximation. Besides the hyperfine interaction also the spin-orbit interactions of lepton and hadron are included. For like charges the Coulomb repulsion reduces strongly the size of polarization observables compared to the plane wave Born approximation whereas for opposite charges the Coulomb attraction leads to a substantial increase of these observables for hadron lab kineti…

Measurement of polarization observables in elastic and inelastic electron-deuteron scattering at the VEPP-3 storage ring.

Relations between polarization observables and complete sets for deuteron photodisintegration

The polarization observables for deuteron photodisintegration are given as Hermitean forms of theT-matrix elementsti. By inversion we are able to express a given productti*tj in terms of polarization observables. This allows (i) to derive linear relations between observables for unpolarized, circularly and linearly polarized photons, (ii) to construct explicitly complete sets of polarization observables, and (iii) to derive quadratic relations between observables.

Photoreactions with tensor-polarized deuterium target at VEPP–3

We give an overview of the activity in studying photoprocesses on a tensor-polarized deuterium target, which is carried out at the VEPP–3 electron storage ring. Recent experimental results on tensor asymmetries in two-body deuteron photodisintegration at the photon energy up to 500 MeV, and in coherent pion photoproduction on deuteron are presented. Plans to upgrade the facility and future experiments are discussed. Further progress is connected with the installation of a tagging system for almost-real photons. This would allow us to extend the measurements of polarization observables in photonuclear reactions on deuteron up to a photon energy of 1.5 GeV and permit to perform double polariz…

Deuteron Compton Scattering

We have calculated deuteron Compton scattering below pion production threshold using different realistic NN potential models and explicit meson exchange current contributions. The gauge conditions for the current and two photon operators have been exploited extensively, so that our model fulfills the low energy theorems. Rescattering, meson exchange and nucleon substructure contributions are studied and compared with a previous calculation and recent experimental data.

Measurements of the electron-helicity asymmetry in the quasi-elastic A(e→,e′p) process

Abstract We present measurements of the electron helicity asymmetry in quasi-elastic proton knockout from 2H and 12C nuclei by polarized electrons. This asymmetry depends on the fifth structure function, is antisymmetric with respect to the scattering plane, and vanishes in the absence of final-state interactions, and thus it provides a sensitive tool for their study. Our kinematics cover the full range in off-coplanarity angle ϕ p q , with a polar angle θ p q coverage up to about 8°. The missing energy resolution enabled us to determine the asymmetries for knock-out resulting in different states of the residual 11B system. We find that the helicity asymmetry for p-shell knockout from 12C d…

Ab initio calculation of Li7 photodisintegration

The Li7 total photoabsorption cross section is calculated microscopically. As nucleon-nucleon interaction the semi-realistic central AV4' potential with S- and P-wave forces is taken. The interaction of the final 7-nucleon system is fully taken into account via the Lorentz Integral Transform (LIT) method. For the calculation of the LIT we use expansions in hyperspherical harmonics (HH) in conjunction with the HH effective interaction (EIHH) approach. The convergence of the LIT expansion is discussed in detail. The calculated cross section agrees quite well with the available experimental data, which cover an energy range from threshold up to 100 MeV.

Charge Form Factor of the Neutron at Low Momentum Transfer from theH→2(e→,e′n)H1Reaction

We report new measurements of the neutron charge form factor at low momentum transfer using quasielastic electrodisintegration of the deuteron. Longitudinally polarized electrons at an energy of 850 MeV were scattered from an isotopically pure, highly polarized deuterium gas target. The scattered electrons and coincident neutrons were measured by the Bates Large Acceptance Spectrometer Toroid (BLAST) detector. The neutron form factor ratio ${G}_{E}^{n}/{G}_{M}^{n}$ was extracted from the beam-target vector asymmetry ${A}_{\mathrm{ed}}^{V}$ at four-momentum transfers ${Q}^{2}=0.14$, 0.20, 0.29, and $0.42\text{ }\text{ }(\mathrm{GeV}/c{)}^{2}$.

General formulae for polarization observables in deuteron electrodisintegration and linear relations

Formal expressions are derived for all possible polarization observables in deuteron electrodisintegration with longitudinally polarized incoming electrons, oriented deuteron targets and polarization analysis of outgoing nucleons. They are given in terms of general structure functions which can be determined experimentally. These structure functions are Hermitean forms of theT-matrix elements which, in principle, allow the determination of allT-matrix elements up to an arbitrary common phase. Since the set of structure functions is overcomplete, linear relations among various structure functions exist which are derived explicitly.

Out-of-plane measurements of the fifth response function of the exclusive electronuclear response

The first measurements of f{sub LT}{sup '}, known as the fifth response function, have been made for the {sup 2}H(e(vector sign),e{sup '}p) and {sup 12}C(e(vector sign),e{sup '}p) reactions. This response is directly related to the imaginary part of the interference between the transverse and longitudinal nuclear electromagnetic currents. Its observation requires longitudinally polarized electron beams and out-of-plane detection, the latter made possible by the newly developed out-of-plane spectrometer system. The initial measurements were made by using a 560-MeV polarized electron beam and quasielastic kinematics at Q{sup 2}=3.3 fm{sup -2}. The development of the methodology for out-of-pla…

Photon Scattering with the Lorentz Integral Transform Method

The application of the Lorentz integral transform (LIT) method to photon scattering off nuclei is presented in general. As an example, elastic photon scattering off the deuteron in the unretarded dipole approximation is considered using the LIT method. The inversion of the integral transform is discussed in detail paying particular attention to the high-energy contributions in the resonance term. The obtained E1-polarizabilities are compared to results from the literature. The corresponding theoretical cross section is confronted with experimental results confirming, as already known from previous studies, that the E1-contribution is the most important one at lower energies.

Energy-weighted M1 sum rule with explicit δ degrees of freedom

Abstract The influence of Δ degrees of freedom on the energy-weighted M1 sum rule is investigated and applied to 2 H and 4 He. Using π- and ρ-exchange potentials a reduction of the potential contribution of the order of 50% is obtained. The absolute value of the sum rule is strongly dependent on the short-range behaviour of the nuclear wave function. Furthermore, the contribution of c.m. effects is evaluated and found to be of the order of 5–10%.

Relativistic effects and spin observables in deuteron electrodisintegration

The influence of relativistic effects in deuteron electrodisintegration, in particular their manifestation in spin observables, is discussed. We have used a simple phenomenological approach by adding the lowest-order relativistic corrections to the nonrelativistic one-body current and including the kinematic wave-function boost. Furthermore, final-state interaction, meson-exchange currents and isobar configurations are included in order to study kinematic regions off the quasi-free case. Sizeable relativistic effects in many observables are found even at low energies.

Exchange currents in electric transitions and the r�le of siegert's theorem: A case study in deuteron photodisintegration

The size of exchange corrections to electric transitions is investigated for deuteron photodisintegration. Large contributions are found in El transitions, which become dominant above 40 MeV. Most of them are already included by using Siegert's theorem together with classical one-body operators. Higher multipoles are only little affected except for rather high energies. The Born approximation for the final states gives in general a poor description.

Photodisintegration of the deuteron in the Δ-resonance region

Abstract Photodisintegration of the deuteron in the Δ-resonance region is calculated treating the final state interaction within a N N−NΔ coupled channel approach including explicit pion degrees of freedom. For the electromagnetic interaction the nucleonic one-body current, meson exchange currents and the direct Δ-excitation are taken into account. The γN Δ-coupling is fixed in accordance with the M 1+ ( 3 2 ) multipole amplitude for pion photoproduction on the nucleon. The resulting total cross section underestimates the experimental data for photon energies below 340 MeV, whereas a good agreement is achieved by uaing a modified γN Δ-coupling effectively including the nonresonant Born term…

Polarization observables in elastic electron deuteron scattering including parity and time reversal violating contributions

The general formalism for polarization observables in elastic electron deuteron scattering is extended to incorporate parity and time reversal violating contributions. Parity violating effects arise from the interference of $\gamma$ and $Z$ exchange as well as from the hadronic sector via a small parity violating component in the deuteron. In addition we have allowed for time reversal invariance violating contributions in the hadronic sector. Formal expressions for the additional structure functions are derived, and their decomposition into the various multipole contributions are given explicitly.

On the Gerasimov-Drell-Hearn sum rule for the deuteron

The Gerasimov-Drell-Hearn sum rule is evaluated for the deuteron by explicit integration up to a photon energy of 550 MeV including contributions from the photodisintegration channel and from coherent and incoherent single pion production as well. The photodisintegration channel converges fast enough in this energy range and gives a large negative contribution, essentially from the $^1S_0$ resonant state near threshold. Its absolute value is about the same size than the sum of proton and neutron GDH values. It is only partially cancelled by the single pion production contribution. But the incoherent channel has not reached convergence at 550 MeV.

The role of the neutron electric form factor ind(e, e? N)N including polarization observables

The influence of the neutron electric form factor on various observables in two-body break-up of deuterons by electrons such as differential cross section, beam, target and beam-target asymmetries and outgoing nucleon polarization as well is investigated for different kinematic regions. The electron-deuteron vector asymmetryAedV and the outgoing nucleon polarization component P′x(n) are the most promising observables in and off the quasi-free region for a determination ofGEn. Also the single polarization observablesAdT and Py0(p) and the double polarization observable P′z(n) show significant influences fromGEn.

η−3Nproblem with separable interactions

The $\eta$-3N-interaction is studied within the four-body Faddeev-Yakubovsky theory adopting purely separable forms for the two- and three-body subamplitudes, limiting the basic two-body interactions to s-waves only. The corresponding separable approximation for the integral kernels is obtained by using the Hilbert-Schmidt procedure. Results are presented for the $\eta$-$^3$H scattering amplitude and for the total elastic cross section for energies below the triton break-up threshold.

Contributions to the electromagnetic form factors of the deuteron from isobar configurations

A nonrelativistic calculation of the elastic electron deuteron scattering has been performed in which the effects arising from nucleon polarization have been systematically investigated. These effects have been taken into account by admixing isobar configurations into the deuteron wave function. Explicit expressions for the various contributions to the respective deuteron form factors have been given. At higher momentum transfers inclusion of the isobar configurations leads to a substantial increase in the form factors which qualitatively appears to account for at least some of the discrepancies between theory and experiment.

Meson and isobar currents in photo absorption and scattering for deuterium

Comment on "Total Cross Section for Photon Absorption by Two Protons inHe3"

A three-body calculation of incoherent $\pi^0$ photoproduction on a deuteron

Incoherent $\pi^0$ photoproduction on a deuteron in the $\Delta(1232)$ region is treated in a three-body scattering approach using separable two-body interactions. Results are presented for total and differential cross sections. It turns out that the role of higher order terms beyond the first order in the multiple scattering series is insignificant, and their inclusion cannot explain the existing discrepancy between theory and experiment.

Atlas of Polarization Observables

Role of pion exchange inηmeson photoproduction on the deuteron

Incoherent $\ensuremath{\eta}$ photoproduction on the deuteron is studied, with the main emphasis on the role of final-state interactions. In addition to the previously studied mechanisms of $NN$ and $\ensuremath{\eta}N$ rescatterings, the role of an intermediate pion exchange is considered in detail, where first a pion is photoproduced on one nucleon and then rescatters into an $\ensuremath{\eta}$ meson on the other, the spectator nucleon. It is found that the role of this pion-mediated contribution is comparable in size to that of $\ensuremath{\eta}N$ rescattering. Results for total and semi-inclusive differential cross sections and associated polarization observables are presented. In pa…

Meson retardation in deuteron electrodisintegration

The effect of meson retardation in $NN$-interaction and exchange currents on deuteron electrodisintegration is studied in a coupled channel approach including $NN$-, $N \Delta$- and $\pi d$-channels. It is shown that the influence of retardation depends on the energy regime: Whereas below $\pi$-threshold calculations with static and retarded operators yield almost identical results, they differ significantly in the $\Delta$-region. Especially, the longitudinal and the longitudinal-transverse interference structure functions are strongly affected.

Polarization-transfer measurement to a large-virtuality bound proton in the deuteron

Possible differences between free and bound protons may be observed in the ratio of polarization-transfer components, $P'_x/P'_z$. We report the measurement of $P'_x/P'_z$, in the $^2\textrm{H}(\vec{e},e^{\prime}\vec{p})n$ reaction at low and high missing momenta. Observed increasing deviation of $P'_x/P'_z$ from that of a free proton as a function of the virtuality, similar to that observed in \hefour, indicates that the effect in nuclei is due to the virtuality of the knock-out proton and not due to the average nuclear density. The measured differences from calculations assuming free-proton form factors ($\sim10\%$), may indicate in-medium modifications.

Subnuclear Degrees of Freedom in Photoabsorption and Scattering

One of the main fields of interest in medium energy nuclear physics is the study of subnuclear or non-nucleonic degrees of freedom (d.o.f.) in nuclei, like meson and isobar or quark-gluon degrees of freedom. It bridges the gap between classical or low energy nuclear physics as understood in terms of nucleon-only degrees of freedom and elementary particle or high energy physics. Hereby one may distinguish roughly two major objectives.

Electromagnetic interactions of nucleons and nuclei at low energy and momentum transfer

The role of electromagnetic form factors in meson exchange currents

The question of electromagnetic form factors, i.e. F1V versus GEV, to be used in isovector meson exchange currents in nonrelativistic calculations is critically reviewed. None of the various arguments given earlier in favour of F1V have been found valid. Furthermore, model dependence of theoretical calculations on deuteron threshold disintegration due to e.m. form factor fits and potential models is found to be substantial. In view of these results, relativistic effects have to be included for a clear understanding of this process in the high momentum transfer region.

From primordial $^4$He abundance to the Higgs field

We constrain the possible time variation of the Higgs vacuum expectation value ($v$) by recent results on the primordial $^4$He abundance ($Y_P$). For that, we improve the analytic models of the key-processes in our previous analytic calculation of the primordial $^4$He abundance. Furthermore, the latest results on the neutron decay, the baryon to photon ratio based on 5-year WMAP observations and a new dependence of the deuteron binding energy on $v$ are incorporated. Finally, we approximate the weak freeze-out, the cross section of photo-disintegration of the deuteron, the mean lifetime of the free neutron, the mass difference of neutron and proton, the Fermi coupling constant, the mass o…

Incoherent pion photoproduction on the deuteron with polarization observables I: Formal expressions

Formal expressions are developed for the general five-fold differential cross section of incoherent $\pi$-photoproduction on the deuteron including beam and target polarization. The polarization observables of the cross section are described by various beam, target and beam-target asymmetries for polarized photons and/or polarized deuterons. They are given as bilinear hermitean forms in the reaction matrix elements divided by the unpolarized cross section. In addition, the corresponding observables for the semi-exclusive reaction $\vec d(\vec \gamma,\pi)NN$ are also given.

Model independent determination of GEn from the reaction

Abstract Electrodisintegration of vector polarized deuterium by longitudinally polarized electrons offers a possibility for measuring the neutron electric form factor G En . In principle, the electron asymmetry is essentially proportional to G En when quasi-free kinematics are employed. We investigate the model dependence of this result by employing several NN force models both with and without meson-exchange and isobar corrections. We find the asymmetry to be remarkably model independent near the neutron quasi-elastic peak.

Exclusive deuteron electrodisintegration with polarized electrons and a polarized target

Exclusive electrodisintegration of the deuteron using a polarized beam and an oriented target is systematically investigated in a nonrelativistic framework. The structure functions are expanded in terms of Legendre functions whose coefficients are quadratic forms in the electric and magnetic multipole moments. Their experimental separation by specific experimental settings is outlined. The structure functions are studied with respect to their sensitivity to the potential model, to subnuclear degrees of freedom, and to electromagnetic form factors in different kinematical regions.

Truncated partial-wave analysis of a complete experiment for photoproduction of two pseudoscalar mesons on a nucleon

A truncated partial wave analysis for the photoproduction of two pseudoscalar mesons on a nucleon is discussed with respect to the determination of a complete set of observables. For the selection of such a set we have applied a criterion previously developed for photo- and electrodisintegration of a deuteron, which allows one to find a 'minimal' set of observables for determining the partial wave amplitudes up to possible discrete ambiguities. The question of resolving the remaining ambiguities by invoking additional observables is discussed for the simplest case, when the partial wave expansion is truncated at the lowest total angular momentum of the final state $J_{max}=1/2$. The resulti…

Tensor Analyzing Powers for Quasi-Elastic Electron Scattering from Deuterium

We report on a first measurement of tensor analyzing powers in quasi-elastic electron-deuteron scattering at an average three-momentum transfer of 1.7 fm$^{-1}$. Data sensitive to the spin-dependent nucleon density in the deuteron were obtained for missing momenta up to 150 MeV/$c$ with a tensor polarized $^2$H target internal to an electron storage ring. The data are well described by a calculation that includes the effects of final-state interaction, meson-exchange and isobar currents, and leading-order relativistic contributions.

Elastic electron deuteron scattering with consistent meson exchange and relativistic contributions of leading order

The influence of relativistic contributions to elastic electron deuteron scattering is studied systematically at low and intermediate momentum transfers ($Q^2\leq 30$ fm$^{-2}$). In a $(p/M)$-expansion, all leading order relativistic $\pi$-exchange contributions consistent with the Bonn OBEPQ models are included. In addition, static heavy meson exchange currents including boost terms and lowest order $\rho\pi\gamma$-currents are considered. Sizeable effects from the various relativistic two-body contributions, mainly from $\pi$-exchange, have been found in form factors, structure functions and the tensor polarization $T_{20}$. Furthermore, static properties, viz. magnetic dipole and charge …

Explanation of Notation

For the presentation of all 288 polarization observables in the next section we have adopted the following scheme. Each observable is a function of the angle and the photon energy. With respect to the latter we have chosen five energies, namely 4.5 MeV, the maximum of the total cross section, 20 MeV, 60 MeV, 100 MeV, and 140 MeV. For each observable and for each of these energies we have studied the following topics: (i) The influence of meson exchange currents (MEC), isobar configurations (IC) and relativistic corrections (RC). Since the various potential models give qualitatively very similar results, we use in this case the r-space version of the Bonn model (OBEPR). (ii) The contribution…

Relativistic Corrections and Unitary Equivalence

Model calculations of the charge and quadrupole deuteron form factors were performed starting from a class of approximately unitary equivalent Hamiltonians and using consistent charge density operators. The approximate unitary equivalence was tested numerically and found to break down already for rather small values of momentum transfer.

The relativistic spin-orbit current in deuteron photodisintegration below and above ?-threshold

It is shown that the spin-orbit current which leads to an improved description ofd(γ,p)n below π-threshold is essentially a two-body exchange effect. This is demonstrated by separation of its one-body contribution. Furthermore, above π-threshold its inclusion leads to an improved agreement with experiment, in particular for the differential cross section in the Δ-excitation region.

Mr. Maxwell's journey into hadron country (electromagnetic currents in nuclei)

In these lectures an introduction is given into the main features of nuclear structure investigations by photoabsorption and electron scattering. After a brief review of the general structure of the electromagnetic interaction, the gauge conditions and low-energy theorems for the electromagnetic interaction operators are discussed. The various theoretical schemes for incorporating subnuclear degrees of freedom either as effective operators like the pion exchange current or explicitely like in the model of nuclear isobar configurations are reviewed. At the end, a few specific experiments are discussed as an illustration of what can be learned from such experiments.

Electromagnetic sum rules in nuclei

Ingredients of Calculation

The calculation is done in the conventional framework of non-relativistic nuclear physics with nucleon, meson and isobar degrees of freedom but the dominant relativistic corrections of lowest order are included as outlined below.

Nucleon polarization in exclusive deuteron electrodisintegration with polarized electrons and a polarized target

Nucleon polarization in exclusive electrodisintegration of the deuteron using a polarized beam and an oriented target is systematically investigated in a nonrelativistic framework but with lowest order relativistic contributions to the one-body current including the kinematic part of the wave function boost. The structure functions and the asymmetries corresponding to the various nucleon polarization components are studied with respect to their sensitivity to the potential model, to subnuclear degrees of freedom, and to relativistic effects in different kinematical regions. Furthermore, a few new observables are found which are very sensitive to the neutron electric form factor ${\mathit{G}…

Role of the D 13 and S 11 Resonances in Deuteron Photodisintegration

The influence of the N(1520) and N(1535) isobar resonances in deuteron photodisintegration is investigated. The isobar configurations are treated in impulse approximation using one-pion exchange for the transition potentials. Isobar admixtures are included in scattering waves as well as in the deuteron. Their influence on the total and differential cross section and various polarization observables, e.g., nucleon polarization and photon asymmetry is small in the Δ resonance region, but not any longer negligible at higher energies.

Relativistic effects in quasifree deuteron electrodisintegration compared to a covariant model

Deuteron disintegration by electrons is calculated in a covariant model for the quasifree region, where final-state interaction and two-body currents can be negiected, and is compared to a phenomenological approach in which one adds to the nonrelativistic one-body current relativistic contributions of lowest order and the kinematic wave-function boost. It is shown that ap/M-reduction of the relativistic theory contains the expressions of the phenomenological approach. The inclusion of relativistic contributions leads to a less frame-dependent description and the deviation from the covariant theory becomes small at low and medium energy and momentum transfers. Furthermore, the dependence of …

Relativistic Effects and Two-Body Currents inH2(e→,e′p)nUsing Out-of-Plane Detection

Measurements of the (2)H((-->)e,e(')p)n reaction were performed with the out-of-plane magnetic spectrometers (OOPS) at the MIT-Bates Linear Accelerator. The longitudinal-transverse, f(LT) and f(')(LT), and the transverse-transverse, f(TT), interference responses at a missing momentum of 210 MeV/c were simultaneously extracted in the dip region at Q2 = 0.15 (GeV/c)(2). In comparison to models of deuteron electrodisintegration, the data clearly reveal strong effects of relativity and final-state interactions and the importance of two-body meson-exchange currents and isobar configurations. We demonstrate that such effects can be disentangled by extracting these responses using the novel out-of…

Final State Interaction Effects in Incoherent Pion Photoproduction on the Deuteron

In the present work [1] incoherent photoproduction of pions on the deuteron in the Δ(1232) resonance region is investigated where besides the impulse approximation (IA) complete two-body rescattering in the nucleon-nucleon (NN) and pion-nucleon (πN) final state subsystems is included (see Fig. 1). The elementary γN → πN amplitude including Born and Δ(1232) resonance contributions is taken from previous work of [2].

Incoherent pion photoproduction on the deuteron with polarization observables II: Influence of final state rescattering

Incoherent pion photoproduction on the deuteron is studied for photon energies from threshold up to 1 GeV with special emphasis on polarization observables. The elementary $\gamma N\to\pi N$ amplitude is taken from the MAID model. The influence of final state interactions on total and semi-exclusive cross sections $\vec d(\vec\gamma,\pi)NN$ is investigated by including complete rescattering in the final $NN$- and $\pi N$-subsystems. For charged pion-production the influence of $NN$-rescattering is moderate whereas $\pi N$-rescattering is almost negligible. Much stronger influences of $NN$-rescattering are seen in neutral pion production, which is due to the elimination of a significant spur…

Polarization Observables in Deuteron Electrodisintegration

The electrodisintegration of the deuteron with polarized beam and target is investigated. The additional polarization form factors (inclusive reaction) and structure functions (exclusive reaction) are discussed. The sensitivity of these form factors and structure functions to the potential model, to meson and isobar degrees of freedom, and to electromagnetic form factors is studied in different kinematical regions.

The Two-Nucleon System beyond the Pion Threshold

A model is developed for the hadronic and electromagnetic interaction in the two-nucleon system above pion threshold in the framework of meson, nucleon and Δ degrees of freedom. It is based on time-ordered perturbation theory and includes full meson retardation in potentials and exchange currents as well as loop contributions to the nucleonic one-body current. Results for some selected processes are discussed.

Comment on the Deuteron Structure FunctionA(q2)at High Momentum Transfers

Calculations of A (q/sup 2/) were performed for various NN potentials and electromagnetic nucleon form factors at q/sup 2/=0--160 fm/sup -2/ with inclusion of isobar configurations and meson exchange currents, indicating that recent elastic electron scattering experiments do not rule out the existence of isobar configurations and meson exchange currents in the deuteron as has been conjectured. (AIP)

The generalized Gerasimov–Drell–Hearn sum rule for deuteron electrodisintegration

The generalized Gerasimov-Drell-Hearn sum rule $I^{GDH}_{\gamma^*d}(Q^2)$ for deuteron electrodisintegration $d(e,e')np$ as function of the squared four-momentum transfer $Q^2$ is evaluated by explicit integration. The calculation is based on a conventional nonrelativistic framework using a realistic $NN$-potential and including contributions from meson exchange currents, isobar configurations and leading order relativistic terms. Good convergence is achieved. The prominent feature is a deep negative minimum, $I_{\gamma^* d}^{GDH}=-9.5$ mb, at low $Q^2\approx 0.2$ fm$^{-2}$ which is almost exclusively driven by the nucleon isovector anomalous magnetic moment contribution to the magnetic dip…

A model study on the nuclear photoeffect

In a simple model of a spinless particle moving in a finite square well potential influences of final state Born approximation and of various approximations in the electromagnetic operators on photoabsorption differential, total and integrated cross sections are investigated. While the Born approximation is very poor in all respects, the long wave length approximation turns out to be the best and reproduces the total cross section quite well. However, appreciable deviations occur in the differential cross section at intermediate energies. The integrated cross section slightly exceeds the classical sum rule resulting from nonanalyticity of the forward compton scattering amplitude, as is disc…

Comment on ‘‘Multinucleon mechanisms in (γ,N) and (γ,NN) reactions’’

Recently, calculations of (\ensuremath{\gamma},NN) cross sections in the \ensuremath{\Delta}(1232) region have been reported by J. Ryckebusch et al. [Phys. Rev. C 49, 2704 (1994)]. However, these calculations use an unjustified ansatz for the \ensuremath{\Delta} propagation, which leads to an underestimation of the (\ensuremath{\gamma},NN) cross section in the resonance region for quasifree kinematics. \textcopyright{} 1996 The American Physical Society.

Meson-retardation effects in deuteron photodisintegration below ?-threshold

Mesor-retardation effects in photodisintegration of the deuteron below pion threshold are studied by constructing retarded one-boson-exchange potentials using time-dependent non-covariant perturbation theory. The corresponding retarded meson-exchange currents including retarded vertex currents are derived analogously by gauge-invariant minimal coupling. It is found that retardation effects in the wave functions and in the electromagnetic currents as well have a significant influence on total and differential cross sections.

Deuteron photodisintegration with the Bonn OBE potentials

The various OBE approximations to the recent Bonn potential are studied in deuteron photodisintegration below π-threshold. Consistent static meson-exchange currents, isobar currents, and the relativistic spin-orbit current are included. Concerning the OBEPT also the leading retardation corrections in the currents are taken into account. Comparison with experimental data is carried out in detail.

Observation of Meson-Exchange Effects in Deuteron Electrodisintegration

Electrodisintegration of the deuteron has been measured for an incident energy of 300 MeV at 30\ifmmode^\circ\else\textdegree\fi{} and 90\ifmmode^\circ\else\textdegree\fi{} scattering angles. The maximum energy transfer was 116 MeV. Very good agreement with theory was achieved when the pionic-exchange currents were included. Near the threshold and for momentum transfer $\stackrel{\ensuremath{\rightarrow}}{\mathrm{q}}_{\mathrm{c}.\mathrm{m}.}^{}{}_{}{}^{2}=3.9$ ${\mathrm{fm}}^{\ensuremath{-}2}$, the meson-exchange currents contribute about 40% to the total cross section.

Subnuclear Degrees of Freedom in Electromagnetic Interactions

Consistent treatment of relativistic corrections in deuteron photodisintegration in a one-pion-exchange model

Using a one-pion-exchange model for the nucleon-nucleon interaction the relativistic corrections to potential and to the electromagnetic operators are derived in a power expansion of (p/M). All corrections up to the order (p/M)3 are consistently included. Numerical results are shown for differential cross section and polarization observables for deuteron photodisintegration. A sizeable influence of relativistic effects on some observables is found even at low energies. A comparison of our operators with the expressions of other authors is given.

Bonn potential and electron-deuteron scattering at high momentum transfer

Deuteron electrodisintegration d(e,e') near threshold is calculated using the various energy-independent Bonn potential versions. At high momentum transfer they lead to rather different results compared to other realistic NN potentials. This can only be partly explained by a different D-state admixture strength. The potential effect is particularly strong for the transverse form factor, but is also present for the longitudinal one. The latter is influenced in a similar way as the longitudinal part of the elastic deuteron form factor A(${\mathit{q}}^{2}$) which we have considered in addition.

Relativistic corrections in quasi-free electro-disintegration of the deuteron

The role of relativistic effects in deuteron break-up by electrons is investigated for quasi-free kinematics by including the lowest-order relativistic corrections beyond the nonrelativistic limit to electromagnetic operators and by wave-function boost. In particular, the dependence of form factors and structure functions on the frame in which they are calculated is studied. It is found that the inclusion of these corrections leads to observables that are less frame-dependent than for a pure nonrelativistic description. The boost contributions show a decisive influence even though they are small in absolute size. Furthermore, the dependence on the parametrization of the nucleon current in t…

Pion exchange current effects inv ? +d??? +p+p

The differential cross sectiondσ/dq2 for the processvμ+d→μ−+p+p is studied using realistic deuteron wave functions and closure over the dinucleon states. The effect of meson exchange currents is estimated using one-pion exchange diagrams in the static limit. Implications of our present results on the determination ofFA(q2) from neutrinodeuteron reaction experiments are discussed.

Electron elastic scattering off a Tensor-polarized Deuterium Internal Target

The tensor analyzing power Γ20 in elastic electron-deuteron scattering has been measured in the four momentum transfer region between 1.4 and 3.2 fm~l using the Internal Target Facility at NIKHEF. Tensor-polarized deuterium is produced in an Atomic Beam Source and injected into a storage cell. Scattered electrons and recoil deuterons were detected in coincidence with two large acceptance nonmagnetic detectors.

Meson exchange and isobar admixture contributions to elastic electron-deuteron scattering

The deuteron structure functions for elastic electron scattering and the deuteron static properties have been calculated with the inclusion of isobar admixtures to the deuteron wave function and meson exchange currents. At higher momentum transfers the structure functions are increased significantly because of the strong enhancement of the deuteron magnetic dipole form factor. Roughly 15–35% of this enhancement depending on the momentum transfer arise from the meson exchange currents.

Exchange currents in the deuteron

The present status of exchange currents and their contribution to deuteron disintegration by real and virtual photons is reviewed. The importance of the Siegert theorem for electric transitions is stressed. Various experiments in photoabsorption, electron and photon scattering with respect to influences of exchange currents are discussed.

Inclusive electron scattering off 4He

Inclusive electron scattering off 4He is investigated for low and medium energy and momentum transfers. The final state interaction, given by the simple semirealistic Malfliet-Tjon potential, is treated rigorously applying the Lorentz Integral Transform (LIT) method. Besides the nonrelativistic one-body current a consistent meson exchange current is constructed and implemented. Results are presented for both longitudinal and transverse response functions at various momentum transfers. Good agreement with experimental data is found for the longitudinal response function, while some strength is missing in the transverse response function on the low-energy side of the quasi-elastic peak.

Separation of theH2(e,e’p) structure functions up to 0.9 GeV/cmomentum transfer

Longitudinal, transverse, and longitudinal-transverse structure functions for the $^{2}\mathrm{H}$(e,e'p) reaction have been determined. Measurements of the cross sections were made in-plane in nearly quasielastic kinematics spanning momentum transfers between 200 and 670 MeV/c and recoil momenta between 0 and 150 MeV/c. In addition, cross sections at momentum transfers above 800 MeV/c were measured at backward scattering angles in aligned kinematics where the response is predominantly transverse. We compared our data with both relativistic and nonrelativistic models. Our results are not consistently in agreement with any of the calculations based on these models. The disagreement between o…

On the variational approach to Jastrow correlations in nuclei

The variational equation determining the Jastrow correlation function is investigated with particular emphasis on the healing problem for both nuclear matter and finite nuclei. The consequences of several healing conditions are discussed. Furthermore, influences from the choice of the single particle basis and from long range correlations are studied and are found to be small in the short range region.

Coherent $\eta$-photoproduction on $^4$He and $^{12}$C in the near-threshold region

Coherent $\eta$ meson photoproduction on $^4$He and $^{12}$C is considered in the near-threshold region. The elementary $\eta$ photoproduction operator includes contributions from the $S_{11}(1535)$ and $D_{13}(1520)$ resonances as well as $t$-channel vector meson exchange and the nucleon pole terms. Due to the suppression of the dominant $S_{11}(1535)$ resonance for spin and isospin saturated nuclei, the reaction is mainly governed by $\omega$ exchange. Furthermore, the influence of Fermi motion and of different prescriptions for the choice of the invariant reaction energy $W_{\gamma N}$ in the elementary amplitude is studied.

Deuteron electrodisintegration near threshold with the Bonn potential

Deuteron electrodisintegration near threshold is calculated for the Bonn potential including consistent meson exchange currents. Experimental data can fairly well be described over the whole q-range if GE is used as electromagnetic form factor for the exchange current, whereas F1 leads to a large overestimation at high q.

Integrated photoabsorption strength and sum rules for a bound Dirac particle

Relativistic effects in the integrated total photoabsorption cross section are discussed using a simple model of a Dirac particle bound in a central potential of scalar or vector type. The integrated strength is calculated explicitly and compared to a new relativistic extension of the TRK-sum rule using positive energy projection and to predictions from dispersion relations. M1 and E2 sum rules are also considered. In all cases the integrated strength exceeds the classical sum rule up to a few percent. The dispersion sum rule cannot be compared directly to the integrated strength since it contains a negative contribution from pair production in the potential field which is of the order of a…

Low-energy scattering and photoproduction ofηmesons on three-body nuclei

The optical potential approach for low-energy scattering of $\eta$-mesons on three-body nuclei is compared to an exact treatment of the $\eta 3N$ system using four-body scattering theory with separable interactions in s-waves only. The higher-order terms including the interaction of the struck nucleon with the surrounding nuclear medium and virtual target excitations in between successive $\eta$-scatterings are found to cause important corrections. Effects of final state interaction in $\eta$-photoproduction on $^3$H and $^3$He are also studied and sizable contributions beyond the optical model approach are found.

Deuteron Photodisintegration below 100 MeV